Differential Kernels for Group Velocity

Abstract

It is shown that the wavenumber dcrivative of the dispersion relation, dω(k)/dk, is a Frkchet differentiable gross Earth datum. The differential kernel functions are given explicitly as expressions quadratic in the normal mode eigenfknctions and their wavenumber derivatives. Explicit expressions for the latter are given as particular solutions to the inhomogeneous propagator equations and as expansions in terms of eigenfunctions. Both spherical stratification and plane stratification are considered in detail. Copyright © 1976, Wiley Blackwell. All rights reserved